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The mathematics of species extinction

Correctly predicting extinction is critical to ecology. Claim extinction too late, and you may be taking resources away from a species that actually could be saved. Claim extinction too early, and you may cause the true extinction due to stopping resources, such as removing protection of its habitat.

There is a balance to be sought, and it's clear that we're not quite there because every year several species that were thought to be extinct are rediscovered. This may seem good news, but it creates a lack of faith for the International Union for Conservation of Nature (IUCN) when it categorises a species as extinct.

Rediscovered species are dubbed Lazarus species, after the character in the bible that came back to life. We have data for some Lazarus mammals, and some mammals that are presumed extinct. What can we infer from the Lazarus mammals to help us establish which presumed-extinct mammals are actually still alive?

Oxford Mathematician Tamsin Lee and colleagues from Australia in a paper published in Global Change Biology use information about the size of the mammal, the search effort it has received, and whether the mammal lived in dense or sparse populations. Some traits, such as the body size, may affect the chances of extinction and rediscovery - large mammals are easier to hunt, but also easier to rediscover. Whereas, factors such as search effort, will only affect the chances of rediscovery. How can we separate and quantify these effects?

To establish which mammals are likely to be rediscovered, and when, the researchers used a model that is commonly used in medicine. Suppose you're conducting a trial for a new medicine which may cure a terminal disease. You give this medicine to 100 subjects, and you make a note of the proportion which are cured. And among those which are not cured, you note how long it takes the patient to die from the disease. You also have notes about, for example, the age of the patients, their gender, cholesterol and whether they're a smoker. From these traits you can establish which patients are most likely to be cured - perhaps young female non-smokers with low cholesterol, followed by young male non-smokers with low cholesterol, and so on. Among those which are not cured, perhaps the medicine prolonged their life, So again, we need to establish which traits created a delay.

Applying this model to the mammal data set, the researchers quantified the effect of traits such as body size, on extinction and rediscovery. They found that indeed, large mammals, such as the Tasmanian Tiger, are more likely to go extinct, as are those mammals that live in dense populations. The effect is compounded for mammals that are both large and live in dense population, such as the Saudi Gazelle which has a 95% chance of being extinct after missing for 79 years. This chance will keep increasing until it reaches 100% in 2039.

Large mammals, which experience a medium search effort (3 to 6 searches) are likely to be rediscovered less than 50 years after they were last seen, whereas small rodent-sized mammals could be missing for over a hundred years, and still be rediscovered. These time limits can be decreased with higher search effort, but search effort has a stronger effect on large mammals. That is, when choosing to allocate resources, searching for a large mammal will enable us to determine the status of the species sooner than when searching for a small mammal. The Saudi Gazelle illustrates this well, since it is a large mammal, but has not reached 100% chance of extinction despite being missing for 79 years. This is because it has received a low search effort.

The strong effect of search effort on large mammals bodes poorly for the Tasmanian Tiger, which was last seen in 1933. There has been a huge search effort, but they did not bear any certain sightings. (The question of certain and uncertain sightings is, as you can imagine, another huge topic in ecology). This implies that since 1983 the Tasmanian Tiger has been truly extinct. However, the Chinese River Dolphin, which has also received a high search effort, has only been missing for 9 years, so it has a 72% chance of being extinct, with this chance not reaching 100% until 2034.

Ulitmately this model demonstrates how even ecology, a relatively new scientific field, is advancing by capitalising upon centuries worth of mathematics.

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